Definable operations on sets and elimination of imaginaries

Holly, Jan

doi:10.1090/S0002-9939-1993-1116261-6

Definable operations on sets and elimination of imaginaries

Author: Jan Holly
Journal: Proc. Amer. Math. Soc. 117 (1993), 1149-1157
MSC: Primary 03C60; Secondary 03C10, 03C40, 03C45, 12L05
DOI: https://doi.org/10.1090/S0002-9939-1993-1116261-6
MathSciNet review: 1116261
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Abstract: This paper gives a new and constructive proof of Poizat's theorem that the theory of algebraically closed fields admits elimination of imaginaries. The proof uses ideas of definability for properties and operations on definable sets. In addition, the property of being finite in an algebrically closed field, as well as the property of having a given algebraic dimension are shown to be definable properties.

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